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The Bi-dimensional space of Korenblum and Composition operator

In: Tatra Mountains Mathematical Publications, vol. 62, no. 1
José Guerrero - Nelson Merentes - José Luíz Sánchez
Detaily:
Rok, strany: 2015, 1 - 12
Kľúčové slová:
$\kappa$-function, $\kappa$-variation, composition operator, regularization, Jensen equation, uniformly continuous and bounded operator
O článku:
In this paper we present the concept of total $\kappa$-variation in the sense of Hardy-Vitali-Korenblum for a real function defined in the rectangle $I^b_a\Bbb\R^2$. We show that the space $\kappa BV(I^b_a,\mathbb R)$ of real functions of two variables with finite total $\kappa$-variation is a Banach space endowed with the norm $||f||_{\kappa}=|f(a)|+\kappa TV(f,I^b_a)$. Also, we characterize the Nemytskij composition operator $H$ that maps the space of functions of two real variables of bounded $\kappa$-variation $\kappa BV(I^b_a, \Bbb R)$ into another space of a similar type and is uniformly bounded (or Lipschitzian or uniformly continuous).
Ako citovať:
ISO 690:
Guerrero, J., Merentes, N., Sánchez, J. 2015. The Bi-dimensional space of Korenblum and Composition operator. In Tatra Mountains Mathematical Publications, vol. 62, no.1, pp. 1-12. 1210-3195.

APA:
Guerrero, J., Merentes, N., Sánchez, J. (2015). The Bi-dimensional space of Korenblum and Composition operator. Tatra Mountains Mathematical Publications, 62(1), 1-12. 1210-3195.